Propagation of partially coherent pulsed beams in the spatiotemporal domain

A generalized model to describe the spatiotemporal partially coherent pulsed beams is presented. The corresponding propagation formula is derived by using the partially coherent light theory. Based on this formula, we obtain a nonstationary generalized ABCD law (which illustrates the transformation of optical beams or pulses passing through media) to describe the spatiotemporal behavior of partially coherent Gaussian pulsed beams. The physical meaning of such generalized pulsed beams is discussed. An example to illustrate the application of this law is given.